Basically, In linux, there are 2 main ways to install software :
-Compile from Source
-Install Binary packages
GCC is what is used when you want to compile software from source tarballs, but the problem is to install GCC from source you need another version of GCC already on your computer, which doesn't seem to be the case.
The other option is to install binary packages. I've never tried Fedora Core, but from what I hear it uses RPMs as binary packages.
Yup ! So What I would suggest is to install GCC using pirut. According to the Fedora Core website, You go into your menu on the desktop, select Application, then Add/Remove programs. Then do a search for GCC, and install the RPMs.
That's about it from my point of view. Maybe someone who has fedora core on this forum can help you better.
But what i'm wondering is why to you need to compile the C++ source ? why not use GNU's equivalent, g++ ?